, Volume 46, Issue 4, pp 385–407 | Cite as

Optimization of fractionation schemes and beamlet intensities in intensity-modulated radiation therapy with changing cancer tumor properties

  • Shraddha GhatkarEmail author
Research Article


Intensity-modulated radiation therapy (IMRT) is a type of external beam radiation therapy used in cancer treatment. In IMRT, the prescribed radiation dose can be administered such that it is maximized on the cancerous tumor while sparing the surrounding healthy tissues. The total dose is divided into fractions across time intervals, called a fractionation scheme. To find the best fractionation scheme and beamlet intensities for total dose, optimization models are used. In this paper, a non-convex mixed-integer nonlinear programming model has been proposed wherein the spatiotemporal changes of the biological properties of the tumor due to tumor cell re-oxygenation, redistribution, and re-population that occur as the treatment progresses have been considered. Also, the dose constraints over both cumulative limits and per-fraction limits have been considered in the model. The output of this model is called the fractionation scheme and beamlet intensities considering biological changes in tumor cells (FBBTs). When the FBBTs are compared with conventional fractionation scheme and beamlet intensities (CFB) which do not include the biological properties of the tumor, it is observed that the FBBTs are more efficacious than the CFBs. To get FBBTs for datasets that resemble realistic tumors, an algorithm based on simulated annealing has been developed and used.


OR in health care Intensity-modulated radiation therapy Fractionation Optimization Simulated annealing 



  1. Aleman D, Kumar A, Ahuja R, Romeijn HE, Dempsey J (2008) Neighborhood search approaches to beam orientation optimization in intensity modulated radiation therapy treatment planning. J Glob Optim 42:587–607CrossRefGoogle Scholar
  2. Bertsimas D, Cacchiani V, Craft D, Nohadani O (2013) A hybrid approach to beam angle optimization in intensity-modulated radiation therapy. Comput Oper Res 40:2187–2197CrossRefGoogle Scholar
  3. Bortfeld, T, Ramakrishnan J, Tsitsiklis JN, Unkelbach J (2013) Optimization of radiation therapy fractionation schedules in the presence of tumor repopulation. arXiv preprint arXiv:1312.1332
  4. Dink D, Langer M, Orcun S, Pekny J, Rardin R, Reklaitis G, Saka B (2011) IMRT optimization with both fractionation and cumulative constraints. Am J Oper Res 1(3):160–171Google Scholar
  5. Ehrgott M, Güler Ç, Hamacher HW, Shao L (2010) Mathematical optimization in intensity modulated radiation therapy. Ann Oper Res 175(1):309–365CrossRefGoogle Scholar
  6. Fowler JF (1989) The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol 62(740):679–694CrossRefGoogle Scholar
  7. Hall EJ, Giaccia AJ (2005) Radiobiology for the radiologist. Lippincott Williams and Wilkins, PhiladelphiaGoogle Scholar
  8. Kim M, Ghate A, Phillips MH (2012) A stochastic control formalism for dynamic biologically conformal radiation therapy. Eur J Oper Res 219(3):541–556CrossRefGoogle Scholar
  9. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680CrossRefGoogle Scholar
  10. Melouk S, Damodaran P, Chang P-Y (2004) Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing. Int J Prod Econ 87(2):141–147CrossRefGoogle Scholar
  11. Morrill S, Lane R, Rosen I (1990) Constrained simulated annealing for optimized radiation therapy treatment planning. Comput Methods Programs Biomed 33:135–144CrossRefGoogle Scholar
  12. Niemierko A (1992) Random search algorithm (RONSC) for optimization of radiation therapy with both physical and biological end points and constraints. Int J Radiat Oncol Biol Phys 23:89–98CrossRefGoogle Scholar
  13. Pawlik TM, Keyomarsi K (2004) Role of cell cycle in mediating sensitivity to radiotherapy. Int J Radiat Oncol Biol Phys 59:928–942CrossRefGoogle Scholar
  14. Powathil G, Kohandel M, Milosevic M, Sivaloganathan S (2012) Modeling the spatial distribution of chronic tumor hypoxia: implications for experimental and clinical studies. Comput Math Methods Med 2012:410602CrossRefGoogle Scholar
  15. Powathil GG, Adamson DJ, Chaplain MA (2013) Towards predicting the response of a solid tumour to chemotherapy and radiotherapy treatments: clinical insights from a computational model. PLoS Comput Biol 9(7):e1003120CrossRefGoogle Scholar
  16. Robert Fourer DMG, Kernighan BW (1990) A modeling language for mathematical programming. Manag Sci 36:519–554CrossRefGoogle Scholar
  17. Ruggieri R, Naccarato S, Nahum AE (2010) Severe hypofractionation: non-homogeneous tumour dose delivery can counteract tumour hypoxia. Acta Oncol 49(8):1304–1314CrossRefGoogle Scholar
  18. Saka B, Rardin RL, Langer MP, Dink D (2011) Adaptive intensity modulated radiation therapy planning optimization with changing tumor geometry and fraction size limits. IIE Trans Healthc Syst Eng 1(4):247–263CrossRefGoogle Scholar
  19. Saka B, Rardin RL, Langer MP (2014) Biologically guided IMRT planning optimization. J Oper Res Soc 65(4):557–571CrossRefGoogle Scholar
  20. Shepard DM, Ferris MC, Olivera GH, Mackie TR (1999) Optimizing the delivery of radiation therapy to cancer patients. SIAM Rev 41(4):721–744CrossRefGoogle Scholar
  21. Stewart BW, Wild CP (eds) (2014) World cancer report. International Agency for Research on Cancer, LyonGoogle Scholar
  22. Tawarmalani M, Sahinidis VN (2005) A polyhedral branch-and-cut approach to global optimization. Math Program 103(2):225–249CrossRefGoogle Scholar
  23. Webb S (1992) Optimization by simulated annealing of three-dimensional, conformal treatment planning for radiation fields defined by a multileaf collimator: II. Inclusion of two-dimensional modulation of the x-ray intensity. Phys Med Biol 37:1689–1704CrossRefGoogle Scholar

Copyright information

© Indian Institute of Management Calcutta 2019

Authors and Affiliations

  1. 1.IIT BombayMumbaiIndia
  2. 2.University of StrathclydeGlasgowUK

Personalised recommendations